Problem
Let $G$ be a simple graph such that for each vertex $v$ of $G$, $\operatorname{deg}(v)\geq 3$. Then show that there is a cycle in $G$ of size not multiple of $3$.
Attempt
Let $P$ be a maximal path of $G$ and $v$ is one of its end point. Now $\operatorname{deg}(v)\geq 3$, so there are tw...
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Proposal: Combine ceiling-function and floor-function, maybe into ceiling-and-floor-functions.
This feels similar to limsup-and-liminf: yes, there are results that deal exclusively with one of the two (for instance, Fatou's Lemma and liminf; or questions about Waring's problem and floors), but th...
